Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-7x-2y &= -3 \\ -2x-y &= 6\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-2x = y+6$ Divide both sides by $-2$ to isolate $x$ $x = {-\dfrac{1}{2}y - 3}$ Substitute this expression for $x$ in the first equation. $-7({-\dfrac{1}{2}y - 3}) - 2y = -3$ $\dfrac{7}{2}y + 21 - 2y = -3$ Simplify by combining terms, then solve for $y$ $\dfrac{3}{2}y + 21 = -3$ $\dfrac{3}{2}y = -24$ $y = -16$ Substitute $-16$ for $y$ in the top equation. $-7x-2( -16) = -3$ $-7x+32 = -3$ $-7x = -35$ $x = 5$ The solution is $\enspace x = 5, \enspace y = -16$.